A single degree of freedom spring mass system with viscous damping has a spring constant of 10 kN/m. The system is excited by a sinusoidal force of amplitude 100 N. If the damping factor (ratio) is 0.25, the amplitude of steady state oscillation at resonance is ________mm.

A solid disc with radius a is connected to a spring at a point $$d$$ above the center of the disc. The other end of the spring is fixed to the vertical wall. The disc is free to roll without slipping on the ground. The mass of the disc is $$M$$ and the spring constant is $$K$$. The polar moment of inertia for the disc about its centre is $$J = {{M{a^2}} \over 2}$$

The natural frequency of this system in rad/s is given by

Which of the following statements are TRUE with respect to heat and work?
$$(i)$$ They are boundary phenomena
$$(ii)$$ They are exact differentials
$$(iii)$$ They are path functions

An ideal gas undergoes a reversible process in which the pressure varies linearly with volume. The conditions at the start (subscript $$1$$) and at the end (subscript $$2$$) of the process with usual notation are:
$${P_1} = 100\,\,kPa,\,\,{V_1} = 0.2\,{m^3}$$ and $${P_2} = 200\,\,kPa,\,\,{V_2} = 0.1\,{m^3}$$
and the gas constant, $$R = 0.275$$ $$kJ/kg$$-$$K.$$ The magnitude of the work required for the process (in $$kJ$$) is _______________